Ad-hoc wireless networks are increasingly becoming important. Much of the work with respect to such networks has been in the area of protocols, but there are important areas that have to do with the physical layer. When an ad-hoc network comprises heterogeneous nodes, each node can use a different modulation, each with a correspondingly different constellation in In-Phase, Quadrature (IQ) space.
There are many reasons for considering such ad-hoc or “multi-drop” networks. One reason is that it would be much easier for an existing point-to-point physical link to join such an ad-hoc network if constellation identification was completely automatic. Thus all the possible constellations would not have to be designed into each node before operation; each node would adapt to the physical layer presented to it from its neighbors. A second reason is that most of the time, synchronization is done using training sequences with a synchronized cooperation between the transmitter and receiver. A third reason is that the physical layer of newly designed nodes in such an ad-hoc network with blind constellation identification could more easily use the most optimal communications channel modulation and coding tricks to efficiently use the available RF spectrum at the required power levels for the desired data rate.
Two standard approaches to constellation classification have been a pattern-recognition or feature-extraction approach, and a non-linearity evaluation and filtering approach.
The first approach relies on a classical concept of “feature” in a feature space, such as a cluster of IQ points. The second approach is based on the observation that raising a signal to an appropriate power and filtering at the right spectral band produces different levels of power depending on the modulation type. The first method is much more targeted and works on general constellations, whereas the second method relies on pre-computed characterizations of particular types of standard constellation sets like Quadrature Phase Shift Keying (QPSK), 8-symbol Phase Shift Keying (8-PSK), 16-symbol Quadrature Amplitude Modulation (16-QAM), etc.
A radon transform method assumes a specific periodic structure to the constellation, while clustering methods apply to general transforms. However, these methods do not easily discover the exact set of symbols in IQ space without some effort in setting thresholds that are sensitive to many parameters of the received signal and constellation type. Also when the signal/noise ratio is too low, the clustering methods fail in very non-uniform ways.